Hello!
So in looking at black hole thermodynamics, I came across the equation
## l_p = \sqrt{G\hbar} ##
But in doing a dimensional analysis of
## \sqrt{G\hbar} ##
I get
## [\sqrt{G \hbar}] = \sqrt{ \frac{Nm^2}{kg^2} \frac{m^3}{kgs} } ##
This obviously doesn't amount to a length. What...
Hi everyone,
So I'm going through a chapter on dual spaces and I came across this:
"A key property of any dual vector ##f## is that it is entirely determined by its values on basis vectors.
## f_i \equiv f(e_i) ##
which we refer to as the components of ##f## in the basis ##{e_i}##, this is...
I just came across this in a textbook: ## (\partial_{\mu}\phi)^2 = (\partial_{\mu}\phi)(\partial^{\mu}\phi) ##
Can someone explain why this makes sense? Thanks.
Looks like it's ## f(x) \approx f(x + \epsilon) - f^1(x + \epsilon)\epsilon ##
Oh, ok, I see now. So the ##\frac{dV}{dx}## is really a ##\frac{dV(x + \epsilon)}{dx}## ??
Hi all,
I was working through a chapter on Lagrangians when I cam across this:
"Using a Taylor expansion, the potential can be approximated as
## V(x+ \epsilon) \approx V(x)+\epsilon \frac{dV}{dx} ##"
Now this looks nothing like any taylor expansion I've seen before. I'm used to
## f(x)...
Hi all,
I was recently watching one of Susskind's 'Theoretical Minimum' lectures in which he says that the entropy of the universe may be measured via the number of observable photons, and that somehow these quantities (photon number and total entropy) are somehow linked. Could anybody with...
Hey all,
So I was watching an MIT OCW video on intro QM and came across this 'clicker' question. (Shows up at 4:45)
Apparently the correct answer is B, but C looks valid to me as well. Could someone explain why C is incorrect?
Thanks
What does it mean for a tensor to have an underlying manifold? And I would think that a linear mapping from a point to a point in vector space would simply be the kronecker delta, but maybe that is a type (1,1) among others?
I was not aware of that. Could you explain further or perhaps point me towards the right resources? I don't understand what it means for a tensor to have a tangent vector space. -_-
Hey all, I'm just starting into GR and learning about tensors. The idea of fully co/contravariant tensors makes sense to me, but I don't understand how a single tensor could have both covariant AND contravariant indices/components, since each component is represented by a number in each index...